I am unsure how to pronounce Tzvi/Tzvia/Tzviya.
I would instinctively pronounce Zibiah as zib-e-uh.
I think that Tabitha is very usable in either the first or middle spot - it doesn't sound christian at all to me, despite it's bible connection. It does slightly remind me of Bewitched, but having met one little Tabitha quite recently and heard of several others, I think that that connotation is becoming less prevalent.
I think the middle spot is the perfect place to go crazy if you're not brave enough to use it in the middle - therefore I think anything can work in the middle.

Tzvia looks pretty. What is the accurate pronunciation? In my head I'm saying zeh-VEE-ah?

tzvee-ya, or zvee-ya. 2 syllables. The -ia is a ya, like Katia or Sonia. Which is a bit tricky. I've seen Tzviya sometimes but I am sort of phobic of adding y's to already-unusual names for fear of looking like I either want to be really kreative or the cat stood on the keyboard, lol.

I think Tabitha is definitely usable as a first name. I know a woman named Tabitha/Tabby. I don't think of it as a specifically Christian name.
I can't say I would intuitively know how to pronounce any of the other names; I've just never encountered them before. However, I think it's totally fine to have something more unusual or difficult to pronounce in the middle spot. People rarely use their middle names anyway.

First of all: my thoughts on Tabitha: I think when posters above are answering about Tabitha, they are comparing Christian vs. secular, not Christian vs. Jewish - from Avram Tzvi I am guessing you are Jewish. Tabitha is very wearable as a secular name, and I certainly wouldn't be shocked to see it on a Jewish girl, nor would many people. BUT the Tabitha of the Bible is of the Christian Bible, she was resurrected by Jesus's follower Peter. The name itself is in fact related to Tzvia from every source I can find - Tzvia is Hebrew for doe or deer and Tabitha is Aramaic for gazelle. Aramaic of course was a language spoken by many people of the ancient middle East (and by a small population today), but is pretty strongly associated with early followers of Jesus. SO - this name could easily have Christian overtones to those of an academic bent. It was also pretty popular among the Puritans. I think you'd be better served to avoid it if you're worried about it ever reading Christian.

Tzvia is beautiful and would make a lovely middle!

Zibiah is pretty intuitive. I do think you'd get zi BYE ah sometimes due to Mariah. Zibia is a little more intuitive. Both spellings and pronunciations are maybe a little close to Tibia, which is hardly the worst thing but maybe a little unfortunate.

Googling around, this name has a million potential spellings. I think Tzvia is best for staying close to Avram Tzvi, and being simple. But there are plenty of options!

Ayla/Ayala/Ayelet are Hebrew origin names that are beautiful to my ear and have meanings also related to does and gazelles, and take the A (and the T in the case of Ayelet) from Avram/Avram Tzvi. Just something to consider.